The Collaboration of a Principal and a Mathematics Specialist

This article describes the importance of the collaboration between the principal, Patty Granada, and the Mathematics Specialist, Susan Garthwaite, in fostering a highly functioning mathematics program. While many aspects of the collaboration as facilitators for a mathematics program are logical, the messy aspects provide greater challenges. Through continued collaboration, they have come to embrace the messiness which has contributed to an awareness of similar belief systems in their roles. These beliefs include openness to learning and a sincere commitment to bringing out the best in students and teachers. The principal and the Mathematics Specialist share their continued journey in this collaborative relationship that is essential to the success of the mathematics program

Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages

Parsimonious modelling of winter season rainfall incorporating reanalysis climatological data

Several Markov Modulated Poisson Process (MMPP) models are developed to describe winter season rainfall with parsimonious parameter use. We propose a methodology for determining the best form of seasonal model for fine-scale rainfall within a MMPP framework. Of those proposed here, a model with a fixed transition rate is shown to be superior over the other MMPP models considered. The model is expanded to include covariate data for sea-level air pressure, relative humidity, and temperature using reanalysis data over 14 years from the coordinates covering the Bracknell rainfall collection site in England. Results are compared using the likelihood ratio test and the second-order properties of aggregated rainfall

Bayes linear kinematics in the analysis of failure rates and failure time distributions

Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times

A new small molecule inhibitor of soluble guanylate cyclase

Soluble guanylate cyclase (sGC) is a haem containing enzyme that regulates cardiovascular homeostasis and multiple mechanisms in the central and peripheral nervous system. Commonly used inhibitors of sGC activity act through oxidation of the haem moiety, however they also bind haemoglobin and this limits their bioavailability for in vivo studies. We have discovered a new class of small molecule inhibitors of sGC and have characterised a compound designated D12 (compound 10) which binds to the catalytic domain of the enzyme with a KD of 11 μM in a SPR assay

PLASIM-ENTSem v1.0: a spatio-temporal emulator of future climate change for impacts assessment

Many applications in the evaluation of climate impacts and environmental policy require detailed spatio-temporal projections of future climate. To capture feedbacks from impacted natural or socio-economic systems requires interactive two-way coupling, but this is generally computationally infeasible with even moderately complex general circulation models (GCMs). Dimension reduction using emulation is one solution to this problem, demonstrated here with the GCM PLASIM-ENTS (Planet Simulator coupled with the efficient numerical terrestrial scheme). Our approach generates temporally evolving spatial patterns of climate variables, considering multiple modes of variability in order to capture non-linear feedbacks. The emulator provides a 188-member ensemble of decadally and spatially resolved (~ 5◦ resolution) seasonal climate data in response to an arbitrary future CO2 concentration and non-CO2 radiative forcing scenario. We present the PLASIM-ENTS coupled model, the construction of its emulator from an ensemble of transient future simulations, an application of the emulator methodology to produce heating and cooling degree-day projections, the validation of the simulator (with respect to empirical data) and the validation of the emulator (with respect to high-complexity models). We also demonstrate the application to estimates of sea-level rise and associated uncertainty

Evaluation of elicitation methods to quantify Bayes linear models

The Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice

First urology simulation boot camp in the United Kingdom

Objective: Simulation is now firmly established in modern surgical training and is applicable not only to acquiring surgical skills but also to non-surgical skills and professionalism. A 5-day intensive Urology Simulation Boot Camp was run to teach emergency procedural skills, clinical reasoning, and communication skills using clinical scenario simulations, endoscopic and laparoscopic trainers. This paper reports the educational value of this first urology boot camp. Subjects and methods: Sixteen urology UK trainees completed pre-course questionnaires on their operative experience and confidence level in common urological procedures. The course included seven modules covering basic scrotal procedures, laparoscopic skills, ureteroscopy, transurethral resection of the prostate and bladder tumour, green light laser prostatectomy, familiarisation with common endoscopic equipment, bladder washout to remove clots, bladder botox injection, setting up urodynamics. Emergency urological conditions were managed using scenarios on SimMan®. The main focus of the course was hands-on training using animal models, bench-top models and virtual reality simulators. Post-course assessment and feedback on the course structure and utility of knowledge gained together with a global outcome score was collected. Results: Overall all the sections of feedback received score of over 4.5/5, with the hands-on training on simulators getting the best score 4.8/5. When trainees were asked “The training has equipped me with enhanced knowledge, understanding and skills,” the average score was 4.9/5.0. The vast majority of participants felt they would recommend the boot camp to future junior trainees. Conclusion: This first UK Urology Simulation Boot Camp has demonstrated feasibility and effectiveness in enhancing trainee’s experience. Given these positive feedbacks there is a good reason to expect that future courses will improve the overall skills of a new urology trainee